Why would you do age verification on login? It only needs to happen once on account creation.
Oops. That slipped my mind. For sites that require log-in, my previous comment is wrong.
I had unconsciously assumed that at least one site would implement the age verification system without requiring users to make accounts to browse the site. In this comment, I will make explicitly make that assumption. For sites without log-in walls but with government-mandated age verification, the concerns in my previous comment would apply. But sites with log-in walls have their own privacy problems independent of age verification, chief being that having to log in means letting the first party site track how often I use the site. A different problem (not necessarily privacy-related, but can be) of log-in walls is that I would be forced to create accounts. If I don't wish to deal with the burden of making accounts, then I won't browse the website. If the website made a log-in wall in response to an age verification mandate from a government, then my First Amendment right to access the speech the website wished to provide will have been chilled.
If you have to verify often enough, and age verification is required on enough sites that are widely used by the general public so that the mere fact that you are using sites that require age verification is not something you might need to hide, I think it would make it much harder to get useful information from log comparisons.